Projections of Planes Questions and Answers

Answer: C

Correct answer: of the inclination only

Tilting a figure about an axis shortens the dimensions measured across that axis, by the cosine of the tilt, while dimensions along the axis are unchanged. That is why an inclined circle becomes an ellipse rather than a smaller circle: one diameter keeps its length and the perpendicular one shrinks.

Answer: D

Correct answer: an ellipse

The diameter lying along the axis of tilt keeps its true length and every diameter perpendicular to it is shortened by the cosine of the inclination, so the circle projects as an ellipse whose major axis is the true diameter and whose minor axis is that diameter foreshortened. Only at ninety degrees does it degenerate into a straight line.

Answer: A

Correct answer: redrawing the views with the figure moved parallel to a plane

The change of position method leaves the planes of projection where they are and moves the figure instead, tilting or turning it in successive stages until it comes parallel to one of them, where it appears in true shape. The auxiliary plane method achieves the same end by leaving the figure alone and moving the plane of projection.

Answer: B

Correct answer: parallel to the figure

A plane of projection parallel to the figure receives it without foreshortening, so the auxiliary view is the true shape directly. The whole art of the method lies in arranging that parallelism, which for a figure inclined to both principal planes takes two steps rather than one.

Answer: C

Correct answer: two successive auxiliary projections

The first auxiliary is taken on a plane perpendicular to the figure, in which the figure appears as a straight line, and this establishes its inclination. The second is then taken parallel to that line, and hence parallel to the figure, giving the true shape. One auxiliary cannot do both, since the direction of the second depends on the result of the first.

Answer: D

Reducing the figure to a line establishes the direction of its plane unambiguously, and the second projection is then taken parallel to that line. Attempting the true shape in one step is what makes such problems go wrong.

Answer: A

Correct answer: perpendicular to that plane of projection

A plane figure projects as a line only when it is seen edge on, which happens when the figure is perpendicular to the plane of projection. This is the observation that drives the auxiliary method: the first auxiliary is chosen precisely to make the figure appear as a line, and the second is taken at right angles to it.

Answer: B

Correct answer: perpendicular to their line of intersection

The dihedral angle must be measured in a plane cutting both faces at right angles to their common edge, since any other section cuts the faces obliquely and gives a larger angle. This is the same reason that an auxiliary view for a dihedral angle is taken with the line of intersection appearing as a point.

Answer: C

Correct answer: its own projection on that plane

The angle between a line and a plane is defined as the angle between the line and its orthogonal projection onto that plane, which is the smallest angle the line makes with any line in the plane. It is the complement of the angle between the line and the plane’s normal, which is why the two are so easily confused.

Answer: D

Correct answer: the traces of that line

A trace of the line is a point where the line meets a plane of projection, and if the line lies in the plane then that point lies in the plane too, and hence on the plane’s trace. So the plane’s horizontal trace passes through the line’s horizontal trace and its vertical trace through the line’s vertical trace - which is how such a plane is constructed.